I need a program to make math visualizations and diagrams. No fancy 3D stuff, just all sorts of geometric diagrams, tiles of different appearances arranged in various ways, lines drawn between points and so on. For example, I'd like to be able to easily draw all the 16 different squares in this picture and drag them around in different ways.

allSimples.png (267 Bytes) Viewed 5290 times

A bonus would be a capability for simple animation: again, nothing complicated, just things appearing and disappearing, moving and rotating from one place to another, maybe color highlights and text annotations appearing and disappearing at the right time.

I know there's Flash, but I don't really feel like learning ActionScript for it.

There's probably plenty of MathCAD suggestions, but maybe GIMP, and using Script-Fu (or GIMP Perl, would be my preference, but I try not to force that on others), although that does sound a lot like the same effort as learning ActionScript that you don't want to do...

But my logic behind that is that you can easily work with layers (to save as frames/framedifs) to do the animation you want, once you've got your head around that.

But there's probably a better alternative that is actually designed to do what you want, and SVG and/or HTML5 canvas manipulation might be yet another answer...